{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Low pass filter\n",
    "\n",
    "The following circuit diagram (from [Wikipedia](https://en.wikipedia.org/wiki/File:RC_Divider.svg)) shows a low-pass filter built with one resistor and one capacitor.  \n",
    "\n",
    "![Low-pass filter circuit diagram](diagrams/RC_Divider.png)\n",
    "\n",
    "A \"filter\" is a circuit takes a signal, $V_{in}$, as input and produces a signal, $V_{out}$, as output.  In this context, a \"signal\" is a voltage that changes over time.\n",
    "\n",
    "A filter is \"low-pass\" if it allows low-frequency signals to pass from $V_{in}$ to $V_{out}$ unchanged, but it reduces the amplitude of high-frequency signals.\n",
    "\n",
    "By applying the laws of circuit analysis, we can derive a differential equation that describes the behavior of this system.  By solving the differential equation, we can predict the effect of this circuit on any input signal.\n",
    "\n",
    "Suppose we are given $V_{in}$ and $V_{out}$ at a particular instant in time.  By Ohm's law, which is a simple model of the behavior of resistors, the instantaneous current through the resistor is:\n",
    "\n",
    "$ I_R = (V_{in} - V_{out}) / R $\n",
    "\n",
    "where $R$ is resistance in ohms.\n",
    "\n",
    "Assuming that no current flows through the output of the circuit, Kirchhoff's current law implies that the current through the capacitor is:\n",
    "\n",
    "$ I_C = I_R $\n",
    "\n",
    "According to a simple model of the behavior of capacitors, current through the capacitor causes a change in the voltage across the capacitor:\n",
    "\n",
    "$ I_C = C \\frac{d V_{out}}{dt} $\n",
    "\n",
    "where $C$ is capacitance in farads (F).\n",
    "\n",
    "Combining these equations yields a differential equation for $V_{out}$:\n",
    "\n",
    "$ \\frac{d }{dt} V_{out} = \\frac{V_{in} - V_{out}}{R C} $\n",
    "\n",
    "Follow the instructions blow to simulate the low-pass filter for input signals like this:\n",
    "\n",
    "$ V_{in}(t) = A \\cos (2 \\pi f t) $\n",
    "\n",
    "where $A$ is the amplitude of the input signal, say 5 V, and $f$ is the frequency of the signal in Hz."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Params and System objects\n",
    "\n",
    "Here's a `Params` object to contain the quantities we need.  I've chosen values for `R1` and `C1` that might be typical for a circuit that works with audio signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "second"
      ],
      "text/latex": [
       "$\\mathrm{second}$"
      ],
      "text/plain": [
       "<Unit('second')>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ohm = UNITS.ohm\n",
    "farad = UNITS.farad\n",
    "volt = UNITS.volt\n",
    "Hz = UNITS.Hz\n",
    "second = UNITS.second"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>R1</th>\n",
       "      <td>1000000.0 ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>1e-09 farad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>5 volt</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f</th>\n",
       "      <td>1000 hertz</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "R1    1000000.0 ohm\n",
       "C1      1e-09 farad\n",
       "A            5 volt\n",
       "f        1000 hertz\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = Params(\n",
    "    R1 = 1e6 * ohm,\n",
    "    C1 = 1e-9 * farad,\n",
    "    A = 5 * volt,\n",
    "    f = 1000 * Hz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can pass the `Params` object `make_system` which computes some additional parameters and defines `init`.\n",
    "\n",
    "* `omega` is the frequency of the input signal in radians/second.\n",
    "\n",
    "* `tau` is the time constant for this circuit, which is the time it takes to get from an initial startup phase to \n",
    "\n",
    "* `cutoff` is the cutoff frequency for this circuit (in Hz), which marks the transition from low frequency signals, which pass through the filter unchanged, to high frequency signals, which are attenuated.\n",
    "\n",
    "* `t_end` is chosen so we run the simulation for 4 cycles of the input signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_system(params):\n",
    "    \"\"\"Makes a System object for the given conditions.\n",
    "    \n",
    "    params: Params object\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    f, R1, C1 = params.f, params.R1, params.C1\n",
    "    \n",
    "    init = State(V_out = 0)\n",
    "    omega = 2 * np.pi * f\n",
    "    tau = R1 * C1\n",
    "    cutoff = 1 / R1 / C1 / 2 / np.pi\n",
    "    t_end = 4 / f\n",
    "    dt = t_end / 4000\n",
    "    \n",
    "    return System(params, init=init, t_end=t_end, dt=dt,\n",
    "                  omega=omega, tau=tau, cutoff=cutoff.to(Hz))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make a `System`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>R1</th>\n",
       "      <td>1000000.0 ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>1e-09 farad</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>5 volt</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f</th>\n",
       "      <td>1000 hertz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>init</th>\n",
       "      <td>V_out    0\n",
       "dtype: int64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>0.004 / hertz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dt</th>\n",
       "      <td>1e-06 / hertz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>omega</th>\n",
       "      <td>6283.185307179586 hertz</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tau</th>\n",
       "      <td>0.001 farad * ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cutoff</th>\n",
       "      <td>159.15494309189532 hertz</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "R1                   1000000.0 ohm\n",
       "C1                     1e-09 farad\n",
       "A                           5 volt\n",
       "f                       1000 hertz\n",
       "init       V_out    0\n",
       "dtype: int64\n",
       "t_end                0.004 / hertz\n",
       "dt                   1e-06 / hertz\n",
       "omega      6283.185307179586 hertz\n",
       "tau              0.001 farad * ohm\n",
       "cutoff    159.15494309189532 hertz\n",
       "dtype: object"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = make_system(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Write a slope function that takes as an input a `State` object that contains `V_out`, and returns the derivative of `V_out`.\n",
    "\n",
    "Note: The ODE solver requires the return value from slope_func to be a sequence, even if there is only one element.  The simplest way to do that is to return a list with a single element:\n",
    "\n",
    "```\n",
    "    return [dV_out_dt]\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def slope_func(state, t, system):\n",
    "    \"\"\"Compute derivatives of the state.\n",
    "    \n",
    "    state: V_out\n",
    "    t: time\n",
    "    system: System object with A, omega, R1 and C1\n",
    "    \n",
    "    returns: dV_out/dt\n",
    "    \"\"\"\n",
    "    [V_out] = state\n",
    "    \n",
    "    R1, C1 = system.R1, system.C1\n",
    "    A, omega = system.A, system.omega\n",
    "    \n",
    "    V_in = A * np.cos(omega * t)\n",
    "    \n",
    "    V_R1 = V_in - V_out\n",
    "\n",
    "    I_R1 = V_R1 / R1\n",
    "    I_C1 = I_R1\n",
    "\n",
    "    dV_out_dt = I_C1 / C1\n",
    "\n",
    "    return [dV_out_dt]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test the slope function with the initial conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5000.0 <Unit('volt / farad / ohm')>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_func(system.init, 0*UNITS.s, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then run the simulation.  I suggest using `t_eval=ts` to make sure we have enough data points to plot and analyze the results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
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      ],
      "text/plain": [
       "success                                                 True\n",
       "message    The solver successfully reached the end of the...\n",
       "dtype: object"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results, details = run_ode_solver(system, slope_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>V_out</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000000</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000001</th>\n",
       "      <td>0.004997467101366766 volt / farad / hertz / ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000002</th>\n",
       "      <td>0.00998974189353765 volt / farad / hertz / ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000003</th>\n",
       "      <td>0.014976632282572247 volt / farad / hertz / ohm</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000004</th>\n",
       "      <td>0.01995794638210714 volt / farad / hertz / ohm</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    V_out\n",
       "0.000000                                                0\n",
       "0.000001  0.004997467101366766 volt / farad / hertz / ohm\n",
       "0.000002   0.00998974189353765 volt / farad / hertz / ohm\n",
       "0.000003  0.014976632282572247 volt / farad / hertz / ohm\n",
       "0.000004   0.01995794638210714 volt / farad / hertz / ohm"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a function you can use to plot `V_out` as a function of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_results(results):\n",
    "    xs = results.V_out.index\n",
    "    ys = results.V_out.values\n",
    "\n",
    "    t_end = get_last_label(results)\n",
    "    if t_end < 10:\n",
    "        xs *= 1000\n",
    "        xlabel = 'Time (ms)'\n",
    "    else:\n",
    "        xlabel = 'Time (s)'\n",
    "        \n",
    "    plot(xs, ys)\n",
    "    decorate(xlabel=xlabel,\n",
    "             ylabel='$V_{out}$ (volt)',\n",
    "             legend=False)\n",
    "    \n",
    "plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If things have gone according to plan, the amplitude of the output signal should be about 0.8 V.\n",
    "\n",
    "Also, you might notice that it takes a few cycles for the signal to get to the full amplitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sweeping frequency\n",
    "\n",
    "Plot `V_out` looks like for a range of frequencies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fs = [1, 10, 100, 1000, 10000, 100000] * Hz\n",
    "\n",
    "for i, f in enumerate(fs):\n",
    "    system = make_system(Params(params, f=f))\n",
    "    results, details = run_ode_solver(system, slope_func)\n",
    "    subplot(3, 2, i+1)\n",
    "    plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At low frequencies, notice that there is an initial \"transient\" before the output gets to a steady-state sinusoidal output.  The duration of this transient is a small multiple of the time constant, `tau`, which is 1 ms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the output ratio\n",
    "\n",
    "Let's compare the amplitudes of the input and output signals.  Below the cutoff frequency, we expect them to be about the same.  Above the cutoff, we expect the amplitude of the output signal to be smaller.\n",
    "\n",
    "We'll start with a signal at the cutoff frequency, `f=1000` Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "system = make_system(Params(params, f=1000*Hz))\n",
    "results, details = run_ode_solver(system, slope_func)\n",
    "V_out = results.V_out\n",
    "plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function computes `V_in` as a `TimeSeries`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_vin(results, system):\n",
    "    \"\"\"Computes V_in as a TimeSeries.\n",
    "    \n",
    "    results: TimeFrame with simulation results\n",
    "    system: System object with A and omega\n",
    "    \n",
    "    returns: TimeSeries\n",
    "    \"\"\"\n",
    "    A, omega = system.A, system.omega\n",
    "    \n",
    "    ts = results.index.values * UNITS.second\n",
    "    V_in = A * np.cos(omega * ts)\n",
    "    return TimeSeries(V_in, results.index, name='V_in')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the input and output look like.  Notice that the output is not just smaller; it is also \"out of phase\"; that is, the peaks of the output are shifted to the right, relative to the peaks of the input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_in = compute_vin(results, system)\n",
    "\n",
    "plot(V_out)\n",
    "plot(V_in)\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='V (volt)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function estimates the amplitude of a signal by computing half the distance between the min and max."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_A(series):\n",
    "    \"\"\"Estimate amplitude.\n",
    "    \n",
    "    series: TimeSeries\n",
    "    \n",
    "    returns: amplitude in volts\n",
    "    \"\"\"\n",
    "    return (series.max() - series.min()) / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The amplitude of `V_in` should be near 5 (but not exact because we evaluated it at a finite number of points)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.0 volt"
      ],
      "text/latex": [
       "$5.0\\ \\mathrm{volt}$"
      ],
      "text/plain": [
       "5.0 <Unit('volt')>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_in = estimate_A(V_in)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The amplitude of `V_out` should be lower."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.8133731785983502 volt/(farad hertz ohm)"
      ],
      "text/latex": [
       "$0.8133731785983502\\ \\frac{\\mathrm{volt}}{\\left(\\mathrm{farad} \\cdot \\mathrm{hertz} \\cdot \\mathrm{ohm}\\right)}$"
      ],
      "text/plain": [
       "0.8133731785983502 <Unit('volt / farad / hertz / ohm')>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_out = estimate_A(V_out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the ratio between them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.16267463571967006 1/(farad hertz ohm)"
      ],
      "text/latex": [
       "$0.16267463571967006\\ \\frac{1}{\\left(\\mathrm{farad} \\cdot \\mathrm{hertz} \\cdot \\mathrm{ohm}\\right)}$"
      ],
      "text/plain": [
       "0.16267463571967006 <Unit('1 / farad / hertz / ohm')>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratio = A_out / A_in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.16267463571967006 dimensionless"
      ],
      "text/latex": [
       "$0.16267463571967006\\ dimensionless$"
      ],
      "text/plain": [
       "0.16267463571967006 <Unit('dimensionless')>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratio.to_base_units()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Encapsulate the code we have so far in a function that takes two TimeSeries objects and returns the ratio between their amplitudes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def estimate_ratio(V1, V2):\n",
    "    \"\"\"Estimate the ratio of amplitudes.\n",
    "    \n",
    "    V1: TimeSeries\n",
    "    V2: TimeSeries\n",
    "    \n",
    "    returns: amplitude ratio\n",
    "    \"\"\"\n",
    "    a1 = estimate_A(V1)\n",
    "    a2 = estimate_A(V2)\n",
    "    return a1 / a2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And test your function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.16267463571967006 1/(farad hertz ohm)"
      ],
      "text/latex": [
       "$0.16267463571967006\\ \\frac{1}{\\left(\\mathrm{farad} \\cdot \\mathrm{hertz} \\cdot \\mathrm{ohm}\\right)}$"
      ],
      "text/plain": [
       "0.16267463571967006 <Unit('1 / farad / hertz / ohm')>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate_ratio(V_out, V_in)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating phase offset\n",
    "\n",
    "The delay between the peak of the input and the peak of the output is call a \"phase shift\" or \"phase offset\", usually measured in fractions of a cycle, degrees, or radians.\n",
    "\n",
    "To estimate the phase offset between two signals, we can use cross-correlation.  Here's what the cross-correlation looks like between `V_out` and `V_in`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "corr = correlate(V_out, V_in, mode='same')\n",
    "corr = TimeSeries(corr, V_in.index)\n",
    "plot(corr, color='C4')\n",
    "decorate(xlabel='Lag (s)',\n",
    "         ylabel='Correlation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The location of the peak in the cross correlation is the estimated shift between the two signals, in seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00221799999999997 second"
      ],
      "text/latex": [
       "$0.00221799999999997\\ \\mathrm{second}$"
      ],
      "text/plain": [
       "0.00221799999999997 <Unit('second')>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "peak_time = corr.idxmax() * UNITS.second"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can express the phase offset as a multiple of the period of the input signal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.001 1/hertz"
      ],
      "text/latex": [
       "$0.001\\ \\frac{1}{\\mathrm{hertz}}$"
      ],
      "text/plain": [
       "0.001 <Unit('1 / hertz')>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "period = 1 / system.f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.2179999999999698 dimensionless"
      ],
      "text/latex": [
       "$2.2179999999999698\\ dimensionless$"
      ],
      "text/plain": [
       "2.2179999999999698 <Unit('dimensionless')>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(peak_time / period).to_reduced_units()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We don't care about whole period offsets, only the fractional part, which we can get using `modf`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.21799999999996977 dimensionless"
      ],
      "text/latex": [
       "$0.21799999999996977\\ dimensionless$"
      ],
      "text/plain": [
       "0.21799999999996977 <Unit('dimensionless')>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frac, whole = np.modf(peak_time / period)\n",
    "frac = frac.to_reduced_units()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can convert from a fraction of a cycle to degrees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "78.47999999998912 degree"
      ],
      "text/latex": [
       "$78.47999999998912\\ \\mathrm{degree}$"
      ],
      "text/plain": [
       "78.47999999998912 <Unit('degree')>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frac * 360 * UNITS.degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Encapsulate this code in a function that takes two `TimeSeries` objects and a `System` object, and returns the phase offset in degrees.\n",
    "\n",
    "Note: by convention, if the output is shifted to the right, the phase offset is negative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def estimate_offset(V1, V2, system):\n",
    "    \"\"\"Estimate phase offset.\n",
    "    \n",
    "    V1: TimeSeries\n",
    "    V2: TimeSeries\n",
    "    system: System object with f\n",
    "    \n",
    "    returns: amplitude ratio\n",
    "    \"\"\"\n",
    "    corr = correlate(V1, V2, mode='same')\n",
    "    corr = TimeSeries(corr, V1.index)\n",
    "    peak_time = corr.idxmax() * UNITS.second\n",
    "    period = 1 / system.f\n",
    "    frac, whole = np.modf(peak_time / period)\n",
    "    frac = frac.to_reduced_units()\n",
    "    return -frac * 360 * UNITS.degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-78.47999999998912 degree"
      ],
      "text/latex": [
       "$-78.47999999998912\\ \\mathrm{degree}$"
      ],
      "text/plain": [
       "-78.47999999998912 <Unit('degree')>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate_offset(V_out, V_in, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sweeping frequency again\n",
    "\n",
    "**Exercise:** Write a function that takes as parameters an array of input frequencies and a `Params` object.\n",
    "\n",
    "For each input frequency it should run a simulation and use the results to estimate the output ratio (dimensionless) and phase offset (in degrees).\n",
    "\n",
    "It should return two `SweepSeries` objects, one for the ratios and one for the offsets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def sweep_frequency(fs, params):\n",
    "    ratios = SweepSeries()\n",
    "    offsets = SweepSeries()\n",
    "\n",
    "    for i, f in enumerate(fs):\n",
    "        system = make_system(Params(params, f=f))\n",
    "        results, details = run_ode_solver(system, slope_func)\n",
    "        V_out = results.V_out\n",
    "        V_in = compute_vin(results, system)\n",
    "        \n",
    "        f = magnitude(f)\n",
    "        ratios[f] = estimate_ratio(V_out, V_in)\n",
    "        offsets[f] = estimate_offset(V_out, V_in, system)\n",
    "    return ratios, offsets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run your function with these frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\\[\\begin{pmatrix}1.0 & 3.1622776601683795 & 10.0 & 31.622776601683793 & 100.0 & 316.22776601683796 & 1000.0 & 3162.2776601683795 & 10000.0\\end{pmatrix} hertz\\]"
      ],
      "text/latex": [
       "$\\begin{pmatrix}1.0 & 3.1622776601683795 & 10.0 & 31.622776601683793 & 100.0 & 316.22776601683796 & 1000.0 & 3162.2776601683795 & 10000.0\\end{pmatrix}\\ \\mathrm{hertz}$"
      ],
      "text/plain": [
       "array([1.00000000e+00, 3.16227766e+00, 1.00000000e+01, 3.16227766e+01,\n",
       "       1.00000000e+02, 3.16227766e+02, 1.00000000e+03, 3.16227766e+03,\n",
       "       1.00000000e+04]) <Unit('hertz')>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fs = 10 ** linspace(0, 4, 9) * Hz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratios, offsets = sweep_frequency(fs, params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot output ratios like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(ratios, color='C2', label='output ratio')\n",
    "decorate(xlabel='Frequency (Hz)',\n",
    "         ylabel='$V_{out} / V_{in}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But it is useful and conventional to plot ratios on a log-log scale.  The vertical gray line shows the cutoff frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_ratios(ratios, system):\n",
    "    \"\"\"Plot output ratios.\n",
    "    \"\"\"\n",
    "    # axvline can't handle a Quantity with units\n",
    "    cutoff = magnitude(system.cutoff)\n",
    "    plt.axvline(cutoff, color='gray', alpha=0.4)\n",
    "    \n",
    "    plot(ratios, color='C2', label='output ratio')\n",
    "    decorate(xlabel='Frequency (Hz)',\n",
    "             ylabel='$V_{out} / V_{in}$',\n",
    "             xscale='log', yscale='log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ratios(ratios, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows the cutoff behavior more clearly.  Below the cutoff, the output ratio is close to 1.  Above the cutoff, it drops off linearly, on a log scale, which indicates that output ratios for high frequencies are practically 0.\n",
    "\n",
    "Here's the plot for phase offset, on a log-x scale:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_offsets(offsets, system):\n",
    "    \"\"\"Plot phase offsets.\n",
    "    \"\"\"\n",
    "    # axvline can't handle a Quantity with units\n",
    "    cutoff = magnitude(system.cutoff)\n",
    "    plt.axvline(cutoff, color='gray', alpha=0.4)\n",
    "    \n",
    "    plot(offsets, color='C9')\n",
    "    decorate(xlabel='Frequency (Hz)',\n",
    "             ylabel='Phase offset (degree)',\n",
    "             xscale='log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_offsets(offsets, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For low frequencies, the phase offset is near 0.  For high frequencies, it approaches 90 degrees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis\n",
    "\n",
    "By analysis we can show that the output ratio for this signal is\n",
    "\n",
    "$A = \\frac{1}{\\sqrt{1 + (R C \\omega)^2}}$ \n",
    "\n",
    "where $\\omega = 2 \\pi f$, and the phase offset is\n",
    "\n",
    "$ \\phi = \\arctan (- R C \\omega)$ \n",
    "\n",
    "**Exercise:** Write functions that take an array of input frequencies and returns $A(f)$ and $\\phi(f)$ as `SweepSeries` objects.  Plot these objects and compare them with the results from the previous section.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def output_ratios(fs, system):\n",
    "    R1, C1, omega = system.R1, system.C1, system.omega\n",
    "    \n",
    "    omegas = 2 * np.pi * fs\n",
    "    rco = R1 * C1 * omegas\n",
    "    A = 1 / np.sqrt(1 + rco**2)\n",
    "    return SweepSeries(A, magnitude(fs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.000000</th>\n",
       "      <td>0.9999802613756332 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.162278</th>\n",
       "      <td>0.9998026663382117 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.000000</th>\n",
       "      <td>0.9980319045036448 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31.622777</th>\n",
       "      <td>0.9808266593818514 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100.000000</th>\n",
       "      <td>0.8467330159648304 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>316.227766</th>\n",
       "      <td>0.4495645925385784 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000.000000</th>\n",
       "      <td>0.15717672547758985 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3162.277660</th>\n",
       "      <td>0.050265590254250286 dimensionless</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10000.000000</th>\n",
       "      <td>0.015913478971147695 dimensionless</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "1.000000          0.9999802613756332 dimensionless\n",
       "3.162278          0.9998026663382117 dimensionless\n",
       "10.000000         0.9980319045036448 dimensionless\n",
       "31.622777         0.9808266593818514 dimensionless\n",
       "100.000000        0.8467330159648304 dimensionless\n",
       "316.227766        0.4495645925385784 dimensionless\n",
       "1000.000000      0.15717672547758985 dimensionless\n",
       "3162.277660     0.050265590254250286 dimensionless\n",
       "10000.000000    0.015913478971147695 dimensionless\n",
       "dtype: object"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = output_ratios(fs, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def phase_offsets(fs, system):\n",
    "    R1, C1, omega = system.R1, system.C1, system.omega\n",
    "\n",
    "    omegas = 2 * np.pi * fs\n",
    "    rco = R1 * C1 * omegas\n",
    "    phi = np.arctan(-rco).to(UNITS.degree)\n",
    "    return SweepSeries(phi, magnitude(fs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>values</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
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       "      <td>-0.3599952627020996 degree</td>\n",
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       "316.227766      -63.284247907949336 degree\n",
       "1000.000000      -80.95693892096232 degree\n",
       "3162.277660       -87.1187796579127 degree\n",
       "10000.000000     -89.08818633038616 degree\n",
       "dtype: object"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi = phase_offsets(fs, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the theoretical results along with the simulation results and see if they agree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(A, ':', color='gray')\n",
    "plot_ratios(ratios, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KQ4N3AVwuFx9//DE23PzbaTlkx0ZS1ezit+sLaOvoDGCVSg1evgbUKGBXH+17gVN+GiwiVwL/B7jUs78ngTdFJMWzyXJgM5AE3AYsF5Exp3pcpfrLyy+/zPvvv8+7775LmNPBPXljSYoIpaiumT98UURnl64jpdSJ8jWgNgDXer0/9LftLuDzfqgjA/hvY8w2Y0yXMeZPQCcw1dOFfRbwoDHGZYx5H3gDuKUfjqtUvzj77LNJSUlh5syZAMSFhXBf3jgiQxxsqqxj+bYS3LrYoVIn5LgzSXh8D3hLRBYAYcDPRGQiMB64wJcdeAbxJvbxkdsY80Svbc8GooGtwDxgb6+ZKnYAs32sXSm/GzlyJHfccUeP234Z0eHcPXMsj67bxYd7D5AUEcqFY9MDWKVSg4tPV1DGmLWAAJ8BfwMigLeAicaY1T4eaz5Q3sdPj67pIjIFeAn4d2NMBVZQNffaVzMQ6eNxlRoQ3uG0Y8cOioqKGJ8YzS3TR2MDXjX7WLuvJnAFKjXI+HoFhTGmEvh/IpIA1BtjTujJrzHmQ+CYE5WJyKVYs1P83BjzS09zE1YgeosEdKCJCkrFxcWsWLGC0NBQvvWtbzErI4GaFhcv7yjj2c3FxIeFIEkxgS5TqaB3suOgsvt7HJSI3Ae8CNxqjPmF10fbgFEi4h1SEz3tSgWdkSNHMnHiRObNm9c9Rur8nFQWZqfQ0eXm9xsK2dfQEuAqlQp+QTEOSkSuAf4bWGSMedX7M2OMATZhPfcKE5FzsSar/cupHlcpf7Db7Vx99dUsWLCgxxipr+aOYEZaHM0dnTyeX0BtqyvAlSoV3IJlHNT3sTpfvCcijV4/l3o+XwpMAiqBZ4BbjDFb+uG4SvmFzWvZjdbWVj744APcXV3celoOY+KjqGl18Zv1BbTqGCmljsrXZ1B+HQdljDn9OJ+XYK1HpdSgs2LFCvbs2UN7ezuLFy/m7plj+PmanZTUt/DU53u4e9ZYnHZdR0qp3oJlHJRSQ9bChQvJyMggLy8PgJiwEO7LG0t0qJOtB+pZtmWvjpFSqg++BtT3gAdE5G0Oj4P6HPgm1gwQSqmjGDFiBLfddhsJCYdvNqRGWWOkQu02Pimt5h+79wewQqWC04mMg5oArOHkx0EpNWx5P5PasmULhYWFjE2I4tbTcrABf9tVzurS6sAVqFQQ8ukZlIi8CTxgjPmxf8tRamgrKiri1VdfJTQ0lLvuuosZ6fFcmzuCF7eV8vyX1hip3JTYQJepVFDw9RbfXEDXDVDqFGVnZzNlyhQWLFhATIw1WHfh6FQW56TS6YYnNxZSWt974hSlhidfe/H9GnheRH4NFAI9RhkaY3TQrFI+sNlsXHnllT1u+QEsnZhFTauL9eW1PL6+gB/MExIjQgNUpVLBwdcrqJ9gXUW9BOQDW4AvvX5VSvnIO5yam5t55513cHd18c1poxmfEE1tazu/yd9Nc7uOkVLDm68BldPHzxivX5VSJ8jtdrNixQpWr17Ne++9R4jDzl0zx5AeFUZZYytPfV5IR1dXoMtUKmB8usVnjCn2dyFKDTc2m43Fixfz1ltvMXfuXACiQp3clzeOh1Ybtlc38NyXe/nmtOwjbgkqNRz42ouvi8ODc3tzYS2Z8SLw4xOd5Vyp4SwzM5Obb765RwAlR4Zxb944Hv5sJ5+V1ZAYHsoVkhnAKpUKDF9v8d2ONYv5ncAMz8/twH7gF1hz6V0B/JcfalRqSPMOp40bN7J7926y4yK5fYY1RmplwX4+2nsgcAUqFSC+9uK7H2uC1n94tW0WkRLgcWPMRBEpB5YDP+rvIpUaDgoLC3njjTcIDQ3l7rvvZmpqHDdMGcWft+xl2da9JISHMDU1LtBlKjVgfL2CysLqXt5bKdZEsode97Wku1LKBzk5OUybNo1FixZ1j5E6e1QyF49No8sNT2/cQ3GdjpFSw4evAfUJ8EsR6Q4gEUkCfg586mlaCuzs3/KUGj5sNhtLlizpnlT2kCUTMpmbmUhbZxe/yd/Ngea2o+xBqaHF14C6DatLeZmIbBcRg3XFlAX8m4hcAvwMvb2n1Cnxfh7V2NjIqlWr6Ozs5KZpo5iYFEO9q4PH83fT1N4RwCqVGhi+ThZbAkzHWsn2GeAJ4BJjzOnGmD3AOmCkMWal3ypVahg5NEZq3bp1vP/++zjtdr51+hiyosPZ39TGazv2BbpEpfzO1ysoPN3HS7GeRf0vsEdEbJ7Pqowx2s1IqX5is9m46KKLyMnJYf78+QBEhji4/fQcHDb4uOQARbVNAa5SKf/yKaBEJFZEVmJNbfQykIY1P98mERnhx/qUGrYyMjL4+te/TnR09OG26AjOG52KG3hxWyldutChGsJ8vYL6FdZChSM4PFHsvUAt8Jgf6lJK0fOZVH5+Pjt37uTScRnEhTkprG1iTVlNAKtTyr98DahLsNaD6r7xbYzZC9wDLPRHYUqpwwoKCli5ciWvvPIKnW0tLJ2YBcCrO8p0Ulk1ZPkaUNH0WmLDw3EC+1BKnaQxY8YwY8YMLr74YqKjo5mbmci4hCgaXB38fVd5oMtTyi98DZe3gB+LSIjnvVtEUoBHgHf8UplSqpvNZuPyyy/ntNNO635/Xe5IbMD7xZWUNfT1/0elBjdfA+oeYCRQDUQC7wJ7gVjgPv+UppQ6mqamJsJaG1gwKpkuN7y4rQS3dphQQ4yvy21UAPNF5Fwg1/O97cA7xhj9W6HUANq3bx/PP/88MTExfP2bt7K+/CCmupH1+2vJy0gIdHlK9RtfJ4sFwBjzAfCBn2pRSvkgNTWVqKgo4uPjcXR1sEQyeWFLCS9vL2VaSixhTkegS1SqXxw1oI6zBlQPxhj9G6HUAHE6ndxyyy1ERERgs9k4KzKSj/YeYG99CysL9nOFZAW6RKX6xbGeQV0GXO75+T7WmKcfAouAs4HvABXAA36uUSnVS2RkZPcYKbvNxvWTRwLwzz2VVDa1BrI0pfrNUa+gvNd+EpGfYK0H9brXJp+KyG6sQbyP+q9EpdTRNDQ08O6775KXl8e8rETWlNWwfFsp9+aNC3RpSp0yX3vxCVaniN72Ys0uoZQKgPz8fDZv3sw777zD0olZRDjtfFlVz6aKukCXptQp8zWg1gAPiUj3cp6ecVAPo50mlAqYM888kxkzZrBkyRLiwkK4bHwGAC9tL6G9syvA1Sl1anwNqNuBKUC5Zz2oHUAJkO75TCkVAKGhoVx++eUkJFjdy8/NTiUjOpyqZhf/3FMR4OqUOjW+rgdVgDX+aSnWUhvPYHWemGWM0XlWlAoS9bUHuS7X6jCxcvd+qltcAa5IqZN3rG7mC4wx/zr03hjTAazy/BztOwuNMe/3b4lKqeNxu9289tprbN26lTvuuIOZ6fFs2F/Ly9tLueP0MYEuT6mTcqyBut8Rke8DvwHeNca097WRiDiBS4G7gWZAA0qpAWaz2YiIiMDhcFBRUcHVk4Qvq+rZsL+W7QfqmZQcG+gSlTphx+pmvkRErgB+DmSLyIfAVuAAYANSsJaBn4fVm+8nxphX/F6xUqpP5557LmeccQZxcVZfpovHpvH6znJe3FbKg2dOwmm3HWcPSgWXY051ZIz5K/BXETkHuBgrjNKALmA/sAF4yBjzcX8VJCJzgE+A8caYIk/bKKxnX3OBSuAeY8zK/jqmUkNBREQEERER3e8X56TxaWkN5Y2tfFBcyfk5aQGsTqkT5+tksR8CH/q1EkBEooHnObKu5Vhd3S8BzgReF5HTjDGF/q5JqcFo9+7dHDx4kGtzJ/Db9QW8sauc2ZmJxIWFHP/LSgWJYFts8LfAa94NIjIBmAU8aIxxeTphvAHcEoD6lAp6VVVVLFu2jLfffpuRIV1MTYmltaOLV3eUBbo0pU7ICc1mfipEJBRI7OMjtzGmQkSuAsYC38Oa+++QXGCvMabJq20HMNtvxSo1iKWkpDBr1iwSEhKIjY3l2twItn+8nTVlNZw9KjnQ5SnlswELKGA+fc860Ski2VizUpyL9XzLWzRW70BvzVgLJyql+nDJJZd0v06NcrA4J5WVBRW8uLWEq5Jt2G3aYUIFv1MOKBFJNcZUHm87z3OsI/5WiIgNa4Xe/2eMKRKR+F6bNAERvdoigcaTq1ip4aWjo4MLRqewpqyGvfUtfBkayvQ4fRalgp9Pz6BEpNMz917v9lHAqXZUGAmcAfxGRGqBYk/7ZhG5HtgGjBIR75Ca6GlXSh1DYWEhTzzxBBvX53PNJGte549rXLR06kLYKvgdayaJ64ArPG9twDMi0tZrs2yg5lQKMMbsBcK9jhsPHASmeXUz3wT8TER+gHWr8CtYXd6VUsfQ1dVFbW0tO3bs4OZ585CkaEx1I5/UuDgt0MUpdRzHuoJ6B+s22qHOCS2e14d+GoG1wBJ/FuixFJiENQbqGay1qbYMwHGVGtTGjRvHtddey80334zdbue63JHYgE31HRTX9X60q1RwOdZMEgeAbwKISBHwSK+edH5hjKml17MqY0wJcJG/j63UUCQi3a+zYiI4Pc7JhroOXtxWwv+dO6F7ZV6lgo2vA3X/U0RiROROYALwU6xu3tuNMXv8WaBSqn+4XC42btzIvIRYtjd2UnCwic/21TAvKynQpSnVJ187SUwADHAvcCcQC1wHbBKR+f4rTynVX1544QXeeustyor2cHai1Yvvle1ltLR3Brgypfrm60wSvwFWGGMmAm0AxpivA3/GGr+klApyc+bMIT09nbi4OCbHOBkTH0W9q4O/79Yl3VRw8jWg5gK/76P9UawZzZVSQS43N5fbbruN5ORkbDYb10+2Oky8X1TJvoaWQJen1BF8DagWILWP9vFAff+Vo5TyF5vNht1++K/8qNgIzhqZTKcblm8rxe3WsVEquPgaUM8BT4jIobFHKSJyOfAksMwvlSml/KKjo4MvvviCF154gSUTMogMcbC9uoHP99cGujSlevA1oP4dWIm1Wm4U1tIXrwB/A37kn9KUUv7Q1dVFYWEhhYWF1B+o5IoJmQCs2F5KW2fvqTCVChxfu5l3AD8Qkf/EmnHcCeweiHFRSqn+FRoaypw5cxARsrKyyHC7+ajkACX1Lawq2M8ST2ApFWg+rwclIucCMcaYrcAU4CUReVBEBnJGdKVUP8jKyiIrKwsAu83G9bkjAXi7sILKpt4zmikVGL6Og7ofWAVMEJGZwJ+AOuAm4CH/laeU8rfKykqSbO3MzUqko8vNiu2lgS5JKcD3K6hvAdcbYz4FbgQ2GGO+5nn9NX8Vp5Tyry+//JKnnnqKt956i6WSRbjTzqbKOr6srAt0aUr5HFCZQL7n9SVYHSYAyrBmlVBKDUI5OTmEhYURFxdHTIidy8ZlAFa383btMKECzNfnR7uB80SkFBiD1XsP4Aas5deVUoNQdHQ09913H+Hh1oo3C0en8klpNeWNrbyzp5KLx6UHuEI1nPl6BfUg8DTwNvCCMWaziPwK+CHazVypQe1QOAE47TauzbUWNvxHwX5qWlyBKkupoweUiPybiEQDGGP+irXy7UxjzI2eTZ4DJhhj3vZ/mUopfysvL+eFF15gRCicnh6Pq7OLV3aUBbosNYwd6wrqMSABrCXfAbcx5otDHxpjNhtjtLuPUkPExx9/TEFBAR999BHXTMoi1G4jv/wgO6obAl2aGqaO9QyqHHhKRNZhLSD4gIg09rWhMea//FGcUmrgnH/++cTHx3P22WcTHh7GRWPT+duucpZvLeHfz5yE064LG6qBdayAugnr2dMlnvfnAx19bOcGNKCUGuQSEhJYvHhx9/sLxqSxuqyassZWPiyuYlFOX/NFK+U/xwqoGOByY0yriOwBFhljqgeoLqVUALndbuoO1nDNpBE8saGQN3btY3ZmArFhIYEuTQ0jx3oG9TKQ7Hmt8/ArNUy0tLTwzDPP8Mc//pHx0SFMSYmlpaOL18y+QJemhpljXUHVAg+KyKdANnCdiPS59pMx5nl/FKeUGnjh4eGEhYXhdDqpra3lq5NGsP3Adj4treaskcmMTYgKdIlqmDhWQH0b+G9gief9j+n7SsoNaEApNUTYbDaWLFlCeHg4oaGhACzOSWVVYQUvbi3hh2cIdpt2mFD+d9SAMsa8gqL1UREAAB50SURBVLXmEyLSBUw2xlQMVGFKqcCJje05g9nF49JZs6+G4vpmPimp5uxRyUf5plL9x9f1oOwAIjIOyMV6drXdGGP8WJtSKsC6urrYsGED0dHRXD0xiz98UcRfTRkz0+OJCtWVdpR/+brcRpSIvATsBFYALwHbROQtEdEb0koNUdu3b2flypWsWrWK6UlRTEiMprG9k7/tKg90aWoY8HUuvl8DU4G5QAQQDszDmuX8F/4pTSkVaLm5ueTm5nLhhRcSGhrKdbkjsdvgw+IqSuqbA12eGuJ8DagrgduNMeuMMW7PzzrgLuBq/5WnlAokm83G1VdfTW5uLjabjRGxEZybnYIb+MvWEtxuHYGi/MfXgLIDB/porwGi+68cpVQwa2lp4fLxGcSEOtl9sIm1+w4GuiQ1hPkaUB8BPxaR0EMNIhIG/D/gY38UppQKLuvXr+fxxx+ndE8hV0omAK/sKKO1ozPAlamhyteAuh9YAJSIyNsi8jZQDMzGGi+llBri2tvbaWtrY9euXcwfkUROXCR1be28uVs7TCj/8CmgjDG7gUnAT4ACYAvw78AkY4yuqKvUMDB79mxuuOEGLrnkEuw2G9dNHokNeHdPJeWNrYEuTw1BPg9kMMYcBH7nx1qUUkHM4XAwduzY7vc58VGcOTKJj0uqWb6thG/njcOmM0yofuTrLT6llOpWX19Pfn4+V0zIJNLpYNuBBjZW1AW6LDXEaEAppU5Ie3s7Tz/9NCtXrqS6vIyvTMgAYMX2Uto6uwJcnRpKNKCUUickJCSEvLw8Jk2aRHx8PAtGpTAiJoLqFhdvF+wPdHlqCDmhybREJBoYD2wDQo0xDf1ViIjMBx7H6oyxD/ihZ8JaRGQU8L9YM1lUAvcYY1b217GVUidmwYIFPZ43XTd5JA9/tpNVhRXMG5FESmRYAKtTQ4Wvc/GFisjvsdaIygeygD+KyJsiEneqRYhIBvAPrE4YMVgzVLzgCSaA5cBmIAm4DVguImNO9bhKqZPTuzPEuPhIZmcm0NHlZsX20gBVpYYaX2/x/QSYD5wFHOpP+jAwGni0H+q4EfjIGPOcZxqld7DGWB0UkQnALOBBY4zLGPM+8AZwSz8cVyl1Curq6lixYgUrV67k6olZhDnsfFFRx5Yq7TChTp2vt/iuAb5ujFkjIm4AY8w6EbkN+JsvO/DMQpHYx0duYCZQJCLLgUVACfB/jTGbReQ8YK8xpsnrOzuwAkwpFUAulwtjDE6nk4ULF3LpuHReNft4cWspPz4rhhCHPuZWJ8/XgEoF+nr6WQ9E+riP+cAHfbR3Ah8Cl+IJQuAK4K8iMg1rrr/e0yY3n8BxlVJ+kpKSwpIlS8jOziYyMpJFOeF8UlpNRVMbz2wq4rbTcnDadWyUOjm+BtRHwH3APZ73bs8V0X8An/iyA2PMh0Cff1JF5B/AW8aYNz1NK0TkHuAioAxriQ9vkUCjj7Urpfxo6tSp3a+ddju3Th/No+t28/n+Wp7eWMjtM3Jw2vVKSp04X//U3AtcIiI7sNaCehYoAs4EvtMPdewAEnq1HQrPbcAoEfEOqYmedqVUENm9ezcZEU6+O3sckSEOvqio48nPC2nX8VHqJPg6F98urO7fvwAeAz4HfgxMMMZs74c6ngfmi8gNImIXka8C04C/eZaV3wT8TETCRORc4CvAX/rhuEqpfvLuu++ybNkyPvroI0bHR/G92eOJCnGwubKe339eiEtDSp0gn6+7jTFtwLPGmAeAn2OtBZXRH0UYYzYBF2PNjF6LdevwSmNMiWeTpVgBWQk8A9xijNnSH8dWSvWPSZMmER4eTmxsLACj4iL53pzxRIc62VJVzxMbCnSmCXVCbL6siCkiecDLwE3Al1hXUOlYAXel17OjoCMio4E97733HiNGjAh0OUoFnHVTAkSk3/ftcrkIDQ3t0VbW0MKv1u6iwdWBJEVzz8yxhDkd/X5sNTiVlpZy3nnnAeQYY4q8P/P1CupR4D3gC+AbWM+HkrCeP/20vwpVSg1u3uHU0GBNNJMVE8EDc8cTF+bEVDfym/UFusih8omvATUT+Ikxpg64HHjTMy7pTaD//xumlBrUSkpK+N3vfscnn1idfDOiI7h/zgTiw0LYWdPIY/m7aWnXkFLH5mtA1QGJIpKMNZ7p0Dx444EqfxSmlBq8qqurcblcVFVVcegxQnp0OA/MHU9ieAgFB5v4df4umjWk1DH4Og7qFeBFrAGypcAqEbkGa3LX5/xUm1JqkDrttNOIj49n1KhRPebtS40K5/65E/jV2l3sqW3m0XW7+M7scUSFnNC81WqY8PUK6tvAU8C/gMXGmHYgFvgV8EM/1aaUGsRGjx6N3TNAt7Ozk88//xy3201KZBgPzB1PSmQoxXXNPLp2F42ujgBXq4KRT/9tMcZ0Ar/u1fYMdM+x5+r/0pRSQ8Xf//53Nm3aRFVVFRdccAFJEWHcP8e6ktpbb/Xy++7sccSEhQS6VBVEfAooEUkFfgTkAof6h9qAME9bvF+qU0oNCVOnTmX37t1MmTKluy0xIpQH5o7nkbW7KG1o4ZG1u/jenPHEakgpD19v8f0BWAJsx1py40ugBWsBwf/0T2lKqaFi7Nix3HfffWRlZfVojw8P5YG5E8iIDmdfYyuPrN1FbWt7gKpUwcbXgDoHuMkYcy+wBfizMeZi4CHgbD/VppQaQkJCDl8ZFRcX88orr9DR0UFcWAj3zxlPVnQ45Y2tPLJ2Jwdb9amB8j2gwoACz+vtwOme189idTtXSimfdHZ28vrrr7N161bWr18PQGxYCN+bO4ERMRFUNLXx8Ge7qGnRkBrufA0og3VrD6yAmud5Hc2RS2EopdRRORwOrr32WmbPns3s2YfXHY0JdXL/nPGMio2gqrmNhz/bSXVLWwArVYHma0D9EviTiHwdeAm4TkSeBZZhdT1XSimfpaWlcdFFF/Xoht7a2kpUqJPvzhnP6LhIDrS4ePizXVQ1a0gNV74ut7EM6znUl8aYnVir30ZihdMtfqtOKTXkdXV18eqrr/Lcc8/R3NxMVIiT78wez5j4KKpbXDz82U4qm1oDXaYKAJ+Hbxtj1ni9fhd41y8VKaWGlebmZioqKmhqaqK+vp7IyEgiQxx8O28cv1m/m90Hm3j4M6sLenp0eKDLVQPI13FQMcD3gelYz5x6LN1ujFnY/6UppYaD6OhovvGNb9DQ0EB6enp3e0SIg/vyxvHb9QXsrGnkkbU7+e7s8WTG6GPv4cLXZ1D/C9wOlGOtBbWh149SSp20mJgYMjMzu98XFxdTW1tLuNPBvbPGMjEphrq2Dh5Zu4uyhpYAVqoGkq+3+C4GLjLGfOzPYpRSqqysjGXLlhEREcGtt95KTEwMd88ay+83FLDtQAOPeKZFGhkbGehSlZ+dyHIbuqyGUsrvkpKSSE9PJycnh+joaADCHHbunjmWKSmxNLo6+NXaXRTXNQe4UuVvJ7Ki7i9EJMGfxSilVHh4ODfccAOXX355j6U6Qhx27jx9DNNT42hq7+TRtbvYU9sUwEqVvx31Fp+IVAFur6ZkoEpE6oAeq4wZY1L9U55SajjyXjq+s7OTN954g9mzZ5OVlcUdp+fw9MY9fFFRx6/X7eK+vPGMTYgKYLXKX471DOr+AatCKaWOYt26dWzevJm9e/dy991343Q4uH3GGJ75Yg8b9tfyWP4u7ps1jnGJ0YEuVfWzowaUMUZXylVKBdzs2bM5cOAAM2fOxOGwVvtx2m3cdloO9k1F5Jcf5LH83dybN5YJiTEBrlb1p2Pd4ovAWtL9KqAN+CvwfWNM/QDVppRSOBwOLrvssh5tra2thIeHc8v00ThsNj7bV8Pj+QXcPXMsk5I1pIaKY3WS+C/gMqx5+B4FLsFaF0oppQKmqKiIxx57jO3bt+Ow27h5ejbzsxJxdXbx2/W72Val/4ceKo4VUFcB1xtjfm6MeRi4GviKiOhyl0qpgCkoKKCtrY2CAmsFILvNxk3TsjlrZBLtXW5+u6GALVV1Aa5S9YdjdZIYAezwep+PFWhpQKk/i1JKqaNZuHAh6enpTJo0qbvNbrNxw5RROGw2Ptx7gCc2FHLHjDFMT4sLYKXqVB3rCsqBV3dyY4wb61lU6FG/oZRSfmaz2Zg8eXL3Uh0dHR0YY7DbbFw/eSQLs1Po6HLz5OeFbNxfG+Bq1anwdaCuUkoFHbfbzauvvsry5cvJz8/HZrNxbe4Izs9JpdPt5umNhWwoPxjoMtVJOt5cfN8QkcZe298gIge8NzLG/L7fK1NKqeOw2WyMGTOG4uJiRo4c2d129cQs7DYbbxdW8D9f7OFWt5u8zMQAV6tO1LECai/wrV5t+4Gbe7W5AQ0opVRA5OXlMWXKFCIiDi/DYbPZWCqZOGw2Vhbs5w9fFNHphrlZGlKDybEG6o4ewDqUUuqkeYdTYWEhhYWFnHfeeSyZkIHDbuPvu8r546Yiutxu5o9ICmCl6kT4vKKuUkoFu9bWVl5++WVaW1vJyMhg8uTJXD4+A4cNXt9ZzrObi+l0uzlrZHKgS1U+0IBSSg0Z4eHhXHHFFezatYvc3Nzu9kvGZeCw2XjV7OP5L/fS5XazYFRKACtVvtCAUkoNKRMmTGDChAnd7zs6OrDZbFw4Nh27zcbLO8p4YUsJHV1uFman9FjSQwWXoAkoEbkZ+HesZT12AN8zxnzi+WwU1rLzc4FK4B5jzMpA1aqUGhw6OztZsWIFDoeDpUuXsnhMGg67jeXbSlm+rZT3iqqYlR7PzIwERsVGaFgFmaAYByUi07Dm+/sKEA+8ALwuIofqWw5sBpKA24DlIjImELUqpQaPmpoaSkpKKC4upr7emqPvvNGp3DR1FLGhTqqa21hVWMFPP93Bj/61jdd2lFFc14zb7T7OntVACJYrqPEcDksb1gwWLQAiMgGYBZxvjHEB74vIG8AtwI8CUKtSapBISUnhpptuwu12k5h4uIv5mSOTmT8iiV01jawvP8iG/bXdYbWqsIKUyDBmpcczKyOBkXplFTADFlAiEgr0NQjBDbwNbAG+5HA4XWCM6RKRXGCvMcZ7becdwGw/l6yUGgLS09N7vN+7dy9paWmEhYUhSTFIUgzXTR557LDKiGdWuobVQBvIK6j5wAd9tHcC6YABvgt8gXV19Lrn1l800NzrO81ApP9KVUoNRUVFRSxbtozU1FRuuumm7qXl7TZbj7DaWdPIBu+wKqhgVUEFqZFhzNSwGjADFlDGmA+xbt8dQUR+B+w3xqz1NP1eRL6BtcRHKRDR6yuRQCNKKXUC4uLiiI6OJiMjg5CQvlcOsttsTEyKYWIfYVXZV1hlJDAyRsPKH4LlGdRIYHevtg6gHdgGjBKRCGNMi+eziZ52pZTyWUJCArfeeiuRkZHdgbJx40YKCgqYM2dO93x+h/QVVuvLD/J5H2E1K8PqDahh1X+CJaDeBH4pIiuw1p36GjAZ+IcxpkRENgE/E5EfYN0q/AowL2DVKqUGraioqB7vN23aRHFxMRMmTOgOqNbWVpxOJ07n4X8ivcPq+j7CamVBBSs1rPpVUASUMeYPIhIH/AVrHNQ24GJjTIlnk6XA/2CNgToA3GKM2RKQYpVSQ8qSJUvYunUrItLd9tlnn7FmzRouuOACTj/99CO+0+PKKtdzG3D/0cNqVkYCIzSsTlhQBBSAMeYR4JGjfFYCXDSwFSmlhoP4+HjOOOOMHm0HDhzA5XIRF3d4Rd7Kykpqa2sZO3YsDoeju91htzEpOYZJyb6EVQKzMuI1rHwUNAGllFLB4qqrrmLhwoU9Aio/P5/169dz1llnsXDhwj6/11dYrS8/yMaKQ2G1n5UF+zWsfKQBpZRSffAe2AvWoN+0tDQmTZrU3bZz5062b9/O6aeffkQHC++wsp5ZNbC+vPaIsEqLCmNmuoZVXzSglFLKB7Nnz2b27J7zA2zevJmtW7eSkpLSHVAdHR3Y7Xbs9sMzyVlhFcuk5NgeYfV5RS0VTUeGVV5GPFkaVhpQSil1shYsWEBycjKTJ0/ubvviiy/44IMPOOecc8jLyzviOycSVtNT40iLCicxIoTE8FASI0IJdzqO2OdQpQGllFInKSUlhXPOOadHW2lpKc3Nzd2zVADU19dTXV1Ndnb2Ma+sTE0DG7zC6p97Ko84ZlSIg8SI0O7ASooI7X6fFBFCbFgI9iFy5aUBpZRS/egrX/kK8+bNIz4+vrtt48aNfPjhh8yaNYtLLrmkz+857DZyk2PJ9Qqr3TWN1LS2U93ioqbFRU2ri6b2TpraWyipb+l7PzYbCeEhVmgdCrDuMLOuxMIGyVWYBpRSSvUjm81GWlpaj7bIyEgSExN7LKRYVlbGpk2bmD59OllZWT229w4rb11uN42uju7AqvaEVk2Li5qWdmpaXTS4OjjQ4uJAi+uoNUaFOHpceSX2uAoLJTbMGRRXYRpQSinlZ3l5ecyaNatH2+bNm8nPz8fpdHYHVFdXFzab7aidI+w2G7Fh1m28nPioPrdp6+zi4KEA6w4vFzWt7Udche09xlWY93Ov3ldiieEhA3IVpgGllFIDoHfozJgxA6fTydSpU7vbdu7cycqVK5k/fz5z5849qeOEOeykR4eTHh3e5+ddbjcNro7u4PK+Cqv2BFmjq4OqZhdVzUe/Cov2PAvLiY/i2tyROO39f8WlAaWUUgGQnp5+xFpVBQUFNDQ00NnZ2d1WVlbGp59+yujRo3t0c6+pqSEmJuaos7Ifjd1mIy4shLgTvAo7HGTtHGx10djeSaPnWdil49KJDw/tc1+nQgNKKaWCxMUXX8z06dN7dLCoqqpi+/btOJ3O7oByuVz89re/xeFw8KMf/aj76mzt2rW0tLQwY8aM7lkwjnfbsC8nchUW5rD7JZxAA0oppYKGzWZjxIgRPdpycnJYunQpMTEx3W0tLS3ExcXhdDp7BM/GjRupqKhARLoD6uOPP+bTTz9lwYIF3XMONjY2sm3bNpKTkxkzZswJ1+l9FeZPGlBKKRXE4uLieswJeKjt29/+Nm63u0f73Llzqa6u7nEF1tTURHt7e49bgZWVlaxatYrs7OweAfXkk08SGhrKDTfcQFhYGGDdYuzo6CAtLY3w8L6vqPxFA0oppQap3rftTjvttCO2ufjiiznvvPN6bBsVFcXMmTN7zDfocrmorKzE4XD0GGT8r3/9i127dnHttdd2L0lijGHDhg1MmjSJGTNm9Pdvq5sGlFJKDXGHroYOSUtL49JLL+3RFhISwr333ktzc3OPMEtJSaGlpaXHVVlFRQW7du0iNTXVr3VrQCmllMJms5GQkEBCQkKP9vPPP/+IbadOnUpqauoR2/Y3DSillFInpK8g8wf78TdRSimlBp4GlFJKqaCkAaWUUiooaUAppZQKShpQSimlgpIGlFJKqaA0HLqZOwD2798f6DqUCgoVFRWANZuAUoHm9W/zEQtMDYeAygD42te+Fug6lFJKHV0GUODdMBwCKh84CygHOo+zrVJKqYHlwAqn/N4f2HrPhquUUkoFA+0koZRSKihpQCmllApKGlBKKaWCkgaUUkqpoKQBpZRSKihpQCmllApKGlBKKaWCkgaUUkqpoDQcZpLwCxFxAs8Bo7BmqbjRGNMa2KoGLxH5NuA0xjwS6FoGIxFJAP4CRAAtwNeMMTWBrWrwEZFY4CUgBtgI3GuM0dkMToKIzAeeMMbMONl96BXUyVsKlBpjzgLWATcEuJ5BS0SeBO4OdB2D3F3Aq8aYc4BXgTsDW86gdSvwpjHmTCAKmBPgegYlz3+YvgeEnMp+NKBO3lzgn57X7wALAljLYPc28NNAFzHI/RZ4wfPaCbQHsJZByxjzKPCU5w5JKlAf4JIGq8eA75/qTjSgTl4sh//wNmDdElAnwRjzeqBrGOyMMXXGmFYRmQJ8C/ifQNc0iNmBrUAyUBLgWgYdEbkLeN8Ys+tU96UBdfLqORxKMVghpVTAiMhcrOdQ1xhjDga6nsHKGNNujBHgz/TDVcAwdA1ws4h8COSIyK9OdkfaSeLkrQMWA+8D5wOfBbYcNZyJSC7wNHCZMaY40PUMViLyA2CLMebvQBO6RM8JM8Z0P+4QkS3GmO+d7L40oE7ey8AlIvIpcAC4NsD1qOHtQayH+s+JCMAbnucp6sQ8j3UOv4t1l+SmANczrOl6UEoppYKSXkF5EZHZWF1MU73apgNPAdOAQuCbxpgjVn5Uh+l57B96HvuHnsdTF6hzqJ0kABGxicitWN3GQ73aQ4G/YQ3ciwd+BvzTM5hP9aLnsX/oeewfeh5PXaDPoQaU5T+xuub2HotzDhBijHnM07NnOVb3068OcH2DhZ7H/qHnsX/oeTx1AT2HGlCWp4wxM4H1vdpzge292nYAUwekqsFHz2P/0PPYP/Q8nrqAnkMNKMAYs+8oH0UDzb3amoFI/1Y0OOl57B96HvuHnsdTF+hzqAF1bE1Yk296iwQaA1DLYKbnsX/oeewfeh5P3YCcQw2oY9sGSK+2iZ525Ts9j/1Dz2P/0PN46gbkHGo382P7ALCJyHeA32HNYD4N+GtAqxp89Dz2Dz2P/UPP46kbkHOoV1DHYIxxARdhnfwa4EfAEmNMVUALG2T0PPYPPY/9Q8/jqRuoc6gzSSillApKegWllFIqKGlAKaWUCkoaUEoppYKSBpRSSqmgpAGllFIqKGlAKaWUCkoaUEoppYKSziShhh0RKQKyj/JxiDGmY+CqCU4iMgv4pTFmoYh8A3jEGJPcx3bPAtHGmKuOsz878BnwdWOM8UPJagjSKyg1XP0QyOj9o+EEIuIA/gdrdoB+YYzpAv4LawVWpXyiV1BquGowxuwPdBFBagnQZYxZ0587Nca8KSKPi8g5xpgP+3PfamjSgFKqFxH5MTAH6w7DXOBeY8xzInI/cA+QBHwB3G+M+czzHSfwEPANwAY8DFwN/M4Y86yIfAisN8bc73UcN3CZMeZNz/tj7f9ZrPV2IoCrgGrgGWPMTz2fO7CuCm8DEoF84G6sedJKgAuMMe95HXs38DNjzJ/6OAX3AK+dxHl7Fripj49+bIz5T8/rvwL3AR+e6P7V8KO3+JTq24XAR1gBtVJEbsf6h/VOYAawEnhfRHI82/8YuNHzswi4HJji68F82D/ArUApMAt4BviJiMz0fPYgcC/wbc/3S4B/AJXA+8B1XseaC2TRRwiJSCxwJvCWr7V7uY+et0wfBaqAP3pt8xawyBPoSh2T/iFRw9WvROTnvdou9br11AI85Hl2goj8EPi+MeYfns//W0TOAe4SkQeAfwN+YoxZ5dn+a8DuE6jnqPsHDl11FRhj/sPz+qeepQ5misjnwLeAnxpjXvMc/y6s0EwAXgAeE5FvGWPageuBN40xdX3UMQPrP6691/VJEpG+FqMLA/4G4Nlfnef4F2JdwV1gjCnx2n4b1mqsE4Etxz4larjTgFLD1UNY/3B7K/N6vccrnKKBUcAfRORpr23CgDYgxfOz4dAHxpgiEfH+h/mofNj/Ibt6fbUBCAGSPcfP9zp+A/A9z/5fA54ELhCRVcA1wB1HKScNaDLGtPZqPwjM7mP7X/Tx+xkPvIgVuB/2+rja82vqUY6vVDcNKDVcHTDGHOsKp8XrtcPz603Axj62az7KPrzDpce6Nr1ucR1v/4e4+jiGzau9z7VzjDGNIvI68FVPTWFYtxD70uXZ5xHtfZ0vEWnAuiI69D4GeB1YZYz5dR/7OfRYofMox1eqmz6DUuo4PLeu9gNZxpjdh344fAurESgG5h36jogkAaO9duMC4rzej/F1/z7WVwmc7nX8CBGpEJE5nqYXgIuxeui97Flwri/7gSgRiTjecXsTERvwPNCB9bysLylex1HqmPQKSinf/BJ4UETKsW6lXY8VIAs8nz8EPCQihYDBuvUV5vX9fOA+EXke6znNo/S8wjre/o/n18B/eAYh78Qaw1TH4SuyfwLtwDexOoAczWbPdtOxBtaeiAc99Z4HxHg6XAC4jDE1ntfTsW4XnsjzOTVMaUAp5ZvHsbp4/xLrOc1O4CpjzKcAxpinPVdNTwLhWN3M53l9/1fAJOBt4ADWP+ajfd2/Dx4GYrB698UAnwKXHLpSMsZ0isgK4Aqs3ol9MsbUi8gnWEFzogF1M1anjM97tf8LOMfz+mzgLWOM3uJTx6VLvivlJyJyAGss07OBrgVARF4GdhtjfnCc7a4G/sMYM62fj2/HuhV6vTHm4/7ctxqa9BmUUkOciCwQkW///3bu0IZhIIYC6O80N0UnCCjtAJkhpDBjdIYOdCSzBCQsqhoQYFXv4bNk9mXLuiRDkveJkk+SW2vtfnErjySLcOIsAQX/75ntH7yp9778eryf149J5qsa2KenV76ft8OBFR8AJZmgAChJQAFQkoACoCQBBUBJAgqAklZ7zHQblcKsmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(phi, ':', color='gray')\n",
    "plot_offsets(offsets, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the phase offsets, there are small differences between the theoretical results and our estimates, but that is probably because it is not easy to estimate phase offsets precisely from numerical results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Consider modifying this notebook to model a [first order high-pass filter](https://en.wikipedia.org/wiki/High-pass_filter#First-order_continuous-time_implementation), a [two-stage second-order low-pass filter](https://www.electronics-tutorials.ws/filter/filter_2.html), or a [passive band-pass filter](https://www.electronics-tutorials.ws/filter/filter_4.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
